Author: Charlotte Hillebrand-Viljoen

Producing lecture notes means that the MSc series will have to take a back seat until the end of the month. In case you’ve been relying on me for your physics fix, here’s a video about “what a physicist sees in a cup of coffee”. Pretty sure physicists see the same as anyone else in a cup of coffee until you put a camera in front of them, but said camera having been provided, I think it’s worth the watch!

So far, this series has been a crash course in the basics of the standard model of particle physics, Feynman diagrams and quantum chromodynamics. We’ve spoken a little about quantum mechanics on the way. Now, so that we can talk about this state of matter known as the colour glass condensate (or CGC for short), we’ll have to think about another really weird part of physics: special relativity. Relativity is really about asking what happens when we change velocity.

Changing velocity doesn’t change the laws of physics: this is why tray tables in aeroplanes make sense. Despite the plane’s tremendous velocity, a cup placed on the table stays on the table, just like it would on the ground. Of course, aeroplane tray tables don’t work during takeoff and landing, but the issue there is the acceleration — the change in the velocity — not the velocity itself. It’s also why many physics experiments can ignore the fact that the Earth is a big rock flying through space at a terrifying speed. (Technically the Earth’s velocity is not constant, particularly because it keeps turning, and this gives rise to effects like the Coriolis force.) This idea — that you can pick an constant velocity and physics will work the same way as at any other constant velocity — is one that every idea of relativity keeps front and centre. In fact, velocity-independence (or “frame-independence”) has become a requirement for anything proposed as a law of physics.

So what does change if you change velocities? Most obviously, the relative velocity of everything else. I may think I’m walking at half a metre per second down the plane aisle, but from the ground you’d say I’m rushing overhead at several hundred kilometres per hour, with a slight modification based on whether I’m walking towards the front or the back of the plane. For centuries, the slight modification was assumed to mean that my velocity relative to you was just the sum of my velocity relative to the plane and the plane’s velocity relative to you. However, when one gets more accurate — historically this came from various attempts to measure and describe light, notably by Maxwell and Michelson and Morley — just adding velocities doesn’t work out. In order to get the best theories of light to square up with the best measurements, velocity had to combine in some way other than simple addition. (One of the results of the new method of combination is that a light wave travels at the same speed — whether you run towards it or away from it, it has exactly the same speed relative to you. This is very weird — but we just said we were going to redefine addition, so we should expect things to be weird.) Simple addition is a very good approximation to the new rule for slow-moving objects, but it’s not so good for very very fast ones. This is why ordinary addition of velocities seems to make perfect sense. It’s only when we start measuring fairly esoteric things (like the speed of light) that we come across the new velocity combination rule.

In all of this messing around with velocity, we’re actually messing around with distance and time too. That shouldn’t be too surprising, since velocity is just distance divided by time. In general, if an object is moving very fast compared to you, then when you measure its length, you’ll get an answer slightly smaller than you would if it wasn’t moving. This is called “length contraction.” It’s very weird, but all the evidence points to it being true. There’s a similar, but opposite effect for time. If two event happen on an object moving very fast compared to you, you’ll measure the time between the events as longer than you would if the object wasn’t moving (compared to you). This is called “time dilation.” Again, it’s very strange, but it’s the least strange thing we can do to make sense of the measurements.

So how does all of this relate back to particle physics? In the simplest sense1, it’s because the particles in a collider like the LHC are hurtling towards each other at very nearly the speed of light. To describe a particle about to enter a collision, we will need to take into account the length contraction and time dilation that it will experience. This is where the colour glass condensate comes in.

A particle travelling very fast will be contracted in the direction it travels. So while we might have said that a round ball is a reasonable approximation of a proton or an atomic nucleus, that round ball now becomes more like pancake. If you like (and we do) you could even say it’s like a sheet of glass. Now our particle pancake is not just length contracted, it’s time dilated. That means that the time between events within the particle is larger than usual — in other words, it changes very very slowly. A similar very slow change is a property that is sometimes attributed to glass, which encourages us to name this slowly-changing particle pancake after a sheet of glass.

The glass is colour glass because, as we said last week, there are going to be lots and lots of gluons around — all of which have colour charge. “Condensate” refers to the huge number of gluons and to the fact that if there are enough gluons (and in the CGC there are), the system becomes saturated, so that adding more gluons doesn’t really change anything.

Now, after a brief detour via special relativity, we have our setup. A target particle (a proton or atomic nucleus) is moving so incredibly fast that it becomes a colour glass condensate particle-pancake. A probe particle travels towards the target and interacts with it — probably punching right through it and probably shattering it. (The “inelastic” in “deeply inelastic scattering” means that the target is probably shattered. And the “deeply” means that it’s really, really probably shattered.) Boom! Now all we need are some equations to calculate the probability of this collision actually happening, and perhaps to tell us what we might get out the other side. And maybe some tools that will allow us to calculate with those equations . . .

1 In a more complicated sense, the new velocity combination rules put time and distance on the same footing, which can’t be done in ordinary quantum mechanics and require the development of ideas like quantum field theory.